Wednesday, 21 September 2011

Who was the first Quant?

Scott Patterson, in his book The Quants, describes Ed Thorp as the 'godfather' of Quants. Without doubt, Thorp heralded the modern age of quantitative finance, but does this mean he was the first Quant?

Many might point to Louis Bachelier as being the original Quant. Bachelier had been born in Le Harve, in Normandy, in 1870. His father was a wine-dealer while his mother came from a banking family. In the six months after graduating from school, both of Bachelier's parents died and he was forced to take over the management of the family firm, Bachelier fils, to provide for his younger siblings. After doing his military service in 1891, Bachelier moved to Paris and became involved in the Paris Stock Exchange. Simultaneously, he enrolled on the mathematics degree at the University of Sorbonne, where Poincare was a professor. He was not a brilliant student but in 1895 he embarked on a doctorate that synthesised the activities being undertaken at the Paris Stock Exchange and the theories of heat and of probability, at the cutting edge of physics at the time. Bachelier then left finance and embarked on an academic career that lasted the following forty years, a career that appears to have been hindered by his early association with the markets.

This, however, is not the career path of a Quant. The likes of Ed Thorp and James Simons had a training in science that they then applied to finance, Bachelier had started working in finance and used this experience as the basis of an academic career: he was a 'reverse-quant'.

The history of reverse-quants is probably more significant than that of Quants. Leonardo Bonacci, better known as Fibonacci, could claim to be the first reverse-quant, taking ideas from contemporary finance to change European culture, by changing not just how merchants undertook their business calculations, but how western science wrote mathematics.

Leonardo's father, Guglielmo Bonacci, was a merchant looking after the Pisan interests in the Algerian port of Bejaia. While we might not imagine that medieval finance was very sophisticated, we would be wrong. The historian Alfred Crosby describes a series of transactions undertaken by an Italian merchant, Datini, which, although they took place two hundred years later, would have been similar to the types of transactions Guglielmo Bonacci would have been involved in. In November 1394 Datini bought wool forward from Mallorca. The wool was sent to Pisa, via Barcelona, in summer 1395, arriving in Italy the following January. Datini sold some wool to a colleague in Florence and processed the the rest into cloth, which he sent to Venice for shipping back to Mallorca for sale in July 1396. However the market in the Balearics was weak and so the cloth was transported to Valencia and North Africa. The last piece of cloth was sold three and a half years after the wool was originally been contracted from the shepherds. Datini would have engaged in forward contracts, loan agreements and transactions in at least five currencies (Arogonese, Pisan, Florentine, Venetian, North African). To make a profit, he needed to be an expert at 'commercial arithmetic', or financial mathematics.

Fibonacci was born in Pisa around 1170 and educated, not only in Bejaia but, as far afield as, Egypt, Syria, Constantinople and Provence. He would write a number of books on mathematics, but his first and most influential was the Liber Abaci('Book of Calculation'), which appeared in 1202. The Liberwas heavily influenced by the Arabic book 'The Comprehensive Book on Calculation by Completion and Balancing' written around 825 CE by al-Khwarizmi, who was himself motivated to write the book because

and his book provided the easiest way of arriving at that number, using al-gabr ('restoration') and al-muqabala('balancing'). Fibonacci collated these Arabic techniques into a single textbook for merchants, such as Datini, facing the increasingly complex financial instruments and transactions emerging at the time.

The impact of the Liber Abaci was enormous. Fibonacci became an adviser to the most powerful monarch of the time, Frederick II, Holy Roman Emperor and King of Sicily. More significant, Abaco or rekoning schools sprang up throughout Europe teaching apprentice merchants how to perform the various complex calculations needed to conduct their business. Pacioli, who taught Leonardo da Vinci maths, was a well known graduate. Less well known is the fact that Copernicus came from a merchant family and in 1526, seventeen years before his more famous, "epoch-making" 'On the Revolutions of the Heavenly Spheres', he wrote 'On the Minting of Coin' about finance.

The practical usefulness of the reckoning schools was that, by using positional numbers and algebra, merchants could execute complex financial calculations that would typically include an illicit interest charge, hidden from the mathematically unsophisticated, university based, Church scholars. The merchant bankers were using mathematics to keep one step ahead of the regulator and the effectiveness of the non-university mathematics would not have been lost on the sharper scholastics, observing market practice.

The most influential single Abacograduate has to be the Dutchman, Simon Stevin. Stevin, who was born in 1548 in Bruges, had originally worked as a merchant's clerk in Antwerp then as a tax official back back in Bruges, where he wrote his first book Tafelen van Interest('Tables of interest') which he published in 1582, before moving to the University of Leiden in 1583. About this time, he was appointed as adviser to Prince Mauritz of Nassau, who was leading the Dutch revolt against the Spanish, and eventually became the Dutch Republic's Finance Minister.

As well as being active in government, Stevin carried out scientific experiments, and it is believed his bookeeping inspired his physics. His most famous experiment showed that heavy and light objects fell to the earth, in the absence of air resistance, at the same speed, an experiment that disproved a belief of Aristotle and is usually attributed to Galileo dropping things from the Tower at Pisa some years later.
One of Stevin's most important posts was as the director of the Dutch Mathematical School, established in 1600 by Mauritz to train military engineers. In this capacity, in 1605, he published a textbook for the School, the 'Mathematical Tradition', which was a comprehensive overview of mathematics and included a whole section on 'Accounting for Princes in the Italian manner'. In a very short period, the Dutch Mathematical School became the centre for merchants' training in north western Europe. This success, in turn, forced the authorities at the University of Leiden, which provided the School with its facilities, to take practical sciences, in particular maths, a bit more seriously. The Dutch Mathematical School would inspire the soldier Descartes to study maths and would train Huygens and a whole generation of European scientists. In addition, it was Stevin's promotion of the use of decimals, to aid accounting, that inspired Newton to think of functions as power-series, giving birth to the discipline of Analysis.

So much for 'reverse-quants'. If a Quant is defined as a someone who moves from an academic career into finance, the most famous Quant is Isaac Newton. Newton essentially finished his work in physics with the publication of Principia in 1687, his last significant work, Optiks, published in English in 1704, was based substantially on research undertaken in the early 1670s. After almost a decade of troubles, Newton moved into finance in April 1696 when he was appointed Warden of the Royal Mint. This was a largely ceremonial post, but Newton took to it so much that he became the Mint's operational manager, its Master, in 1699 (see Isaac Newton: Financial Regulator).

Being Master gave Newton an average income some 16 times what he would have had as an academic. Today a 'starting' salary for a jobbing professor in England is around £60,000, and we could expect the Lucasian Professor at Cambridge to earn somewhat more than this. On this basis, the equivalent salary for Newton as Master of the Mint is in excess of £1 million, which pretty well places him in the bulge bracket. Newton, no longer needing the income from his position in Cambridge, resigned his Professorship at the end of 1701. Newton did become President of the Royal Society in 1703, an institution whose foundations were laid by the banker Thomas Gresham, and Newton followed in the footsteps of his patron, the the English Chancellor of the Exchequer, Charles Montagu. Gresham and Montagu, central to the establishment of the oldest national academy of sciences, are just two more examples of 'reverse-quants'.

Newton might be the most famous Quant, but he was not unique or the first. Huygens identified conditional expectation while investigating the pricing of life annuities, and J. Bernoulli identified the number ewhen investigating interest payments. Generations before Huygens, Bernoulli and Newton, we have Galileo, who was born in Pisa around 1564. He was appointed to the Professorship of Mathematics the prestigious University of Padua in 1592, where he made his famous astronomical observations. Galileo had been short of money all his adult life, as a mathematician he was poorly paid and was expected to supplement his salary by taking private students, but this interfered with his research. In 1613 the Duke of Tuscany, Cosimo II de Medici, offered Galileo the position of 'First and Extraordinary Mathematician of the University of Pisa and Mathematician to his Serenest Highness (i.e. Cosimio)' with a large salary and no duties, an ideal post for Galileo. It was some time in the next decade or so that Galileo wrote 'Upon the Discoveries of Dice', which he was almost certainly asked to write by Cosimo, who may have been trying to solve a practical problem in gambling. Galileo did not leave Padua to work in finance, but he did become the mathematical adviser to the the head of one of Italy's most important banking families. Ironically, had Galileo stayed at Padua, under the protection of the religiously ambivalent Venetians, he would never had faced the Inquisition, and possibly would not have become as famous as he is today.

European science did not start in the Renaissance, it existed in the High Middle Ages. The 'renaissance' of the 'long twelfth century' resulted in what the historian Joel Kaye describes as

the transformation of the conceptual model of the natural world ,..., [which] was strongly influenced by the rapid monetisation of European society taking place [between 1260-1380].

and played a pivotal role in the development of European science. Thirteenth century scholars

[were] more intent on examining how the system of exchange actually functioned than how it ought to function..

It seems that Fibonacci did not just influence medieval merchants, those scholars keeping an eye on merchant's dubious dealings, also, became obsessed with mathematics. This included the great scholastic scientist, Albert the Great, and the mathematically minded theologian, Thomas Aquinas. But the most famous scholars to turn to mathematics were the 'Merton Calculators'.

The first of the Calculators was Thomas Bradwardine, who entered Merton College in Oxford in 1323. While studying the quadrivium, mathematics, astronomy, music and geometry, Bradwardine observed that

[Mathematics] is the revealer of genuine truth, for it knows every hidden secret and bears the key to every subtlety of letters. Whoever, then, has the effrontery to pursue physics while neglecting mathematics should know from the start that he will never make his entry through the portals of wisdom.

This was a highly significant point in the history of science since it is the first time that scholars in the Hellenistic tradition, which included Jewish, Christian and Islamic philosophers, innovated in physics by using mathematics. In the footsteps of Bradwardine there was, amongst others, William Heytesbury, who identified the mean speed theorem, and Nicolas Oresme, who introduced the idea of the graph and advised the French king on money supply.

After twelve years at Merton, Bradwardine left the Oxford University to work for the Bishop of Durham, who was the Treasurer and Chancellor of England. So Bradwardine was not only the first Physicist, as we would understand the term today, he was also the first person who left an academic career to take up one in finance. The first Quant was the first Physicist.

Looking at the relationship between scientists and finance reveals some important facts. Firstly, the migration from academic careers in science to finance appear to be embedded, it is not a modern phenomena. However, possibly more significant is the less well-appreciated role of the 'reverse-quants' in the development of science. The influence is captured by events in France in 1304-1305 when economic instability and a market failure led the French King, Philip the Fair, to issue decrees fixing the price of bread. His decrees failed spectacularly, and this was seen by contemporary observers as evidence that 'nature' ruled, and not the authority of the King, and that market prices where an objective, 'scientific' measure. This enabled the likes of Bradwardine to re-assess the role of mathematics in science. Later, people trained in commercial arithmetic - financial mathematics - such as Copernicus and Stevin, were able to challenge the authority of Aristotelian science, and argue that the Earth revolved around the Sun and that heavy and light objects fall at the same speed. Today, financial markets challenge assumptions about determinism and stability of systems, the question is, can science meet those challenges?

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About Me

I am a Lecturer in Financial Mathematics at Heriot-Watt University in Edinburgh. Heriot-Watt was the first UK university to offer degrees in Actuarial Science and Financial Mathematics and is a leading UK research centre in the fields.

Between 2006-2011 I was the UK Research Council's Academic Fellow in Financial Mathematics and was involved in informing policy makers of mathematical aspects of the Credit Crisis.